Compressive load carrying bearings

ABSTRACT

A compressive load carrying laminated bearing comprising alternating bonded layers of a resilient material and a non-extensible material generally concentrically disposed about a common center with successive layers being disposed at successively increasing radii. The fatigue life thereof, when subjected to cylic rotational or torsional motion about the common center, is substantially enhanced by progressively increasing the thickness of the layers of resilient material with increasing radii while simultaneously progressively decreasing the modulus of elasticity of the layers of resilient material with increasing radii. .Iadd.

This Application is a Reissue of Ser. No. 147,488 filed 5/27/71 nowpatent 3,679,197. This Application is also a continuation of ReissueApplication 893,886 filed 4/6/78 now abandoned. .Iaddend.

This invention relates to compressive load carrying bearings and moreparticularily to laminated bearings comprising alternating bonded layersof a resilient material such as an elastomer and non-extensible materialsuch as metal.

It has been shown that the compressive load carrying ability or capacityof a layer of resilient material in a direction perpendicular theretomay be increased many times through the inclusion of spaced parallellaminate of non-extensible material while the yielding capacity in thatdirection is correspondingly reduced. That is, a given thickness ofrubber for instance loses its compressive resilience increasingly withthe increased number of layers it is divided by parallel laminae ofnon-extensible material. At the same time its compressive load carryingcapacity in that direction increases proportionately. However, theability of the resilient material to yield in shear or torsion in adirection along the layers is almost completely unaffected by thelaminations and is essentially the same whether the rubber is in onelayer or a plurality of layers separated by layers of non-extensiblematerial. For a more detailed understanding of such laminated bearingsand basic factors to be considered in their design, reference is made toWildhaber, U.S. Pat. No. 2,752,766 and Hinks, U.S. Pat. No. 2,900,182.

The above briefly described bearing concept has begun to find widecommercial acceptance in bearings characterized in their ability tocarry relatively large compressive loads generally perpendicular to thelayers while simultaneously being relatively soft in shear and/ortorsion along the layers so as to readily accommodate relative movementin designated directions.

While the concept may be employed in bearings of a variety ofconfigurations, depending on the compressive loads to be carried and themotions to be accommodated, many are constructed such that thealternating bonded layers of resilient material and non-extensiblematerial are generally concentrically disposed about a common centerwith successive layers being disposed at successively increasing radii.Such configurations include cylindrical, conical, spherical, sectors ofcylinders, cones and spheres, etc. Due to the configuration and use ofthese bearings to carrying large compressive loads while accommodatingcyclic torsional motion about the common center, greater compressivestresses and shear stresses and strains are established in the resilientlayers closest to the common center as compared to resilient layers moreremote from the common center. In the normal case, these bearings areconstructed with the layers of resilient material having the samemodulus of elasticity, thickness and length. The prolonged use of such abearing in accommmodating cyclic torsional motion results in failurefrom fatigue preferentially at the innermost resilient layer.Accordingly, the fatigue life of such a bearing is typically determinedby the stresses and strains established during use in the innermostresilient layer.

It is an object of the present invention to improve the fatigue life ofa laminated bearing comprising alternating bonded layers of resilientmaterial and non-extensible material generally concentrically disposedabout a common center with successive layers being disposed atsuccessively increasing radii.

Briefly, the object of the present invention is accomplished byprogressively increasing the thickness of the layers of resilientmaterial with increasing radii while simultaneously progressivelydecreasing the modulus of elasticity of the layers of resilient materialwith increasing radii.

One of the objects of the invention having been stated, other objectswll appear as the description proceeds, when taken in connection withthe accompanying drawings, in which:

FIG. 1 is a schematic plan view of a prior art laminated bearing;

FIG. 2 is a schematic plan view of a laminated bearing similar to thatof FIG. 1 incorporating the present invention;

FIG. 3 graphically illustrates the effect of shape factor on allowablecompressive stress; and

FIG. 4 diagramatically illustrates shear strain distribution in alaminated bearing.

With reference to FIG. 1, there is shown a conventional prior artlaminated bearing 10 comprising an inner member 11 having an outwardlyfacing convex surface and an outer member 12 radially spaced from theinner member 11 and having an inwardly facing concave surface. Betweenand bonded to the members 11 and 12 are alternating bonded layers 13 and14 of a resilient material such as an elastomer and a non-extensiblematerial such as metal, respectively. The convex and concave surfacesand each of the layers 13 and 14 are concentrically disposed about acommon center. Bearing 10 is in the form of a sector of a cylinder witheach of layers 13 or resilient material having a generally uniformlength. The layers 13 of resilient material are of uniform thickness andthe resilient material of each layer 13 has the same modulus ofelasticity. It will be apparent that the mean circumferential area ofeach layer 13 of resilient material increases with radii. Thus, theshape factor or ratio between effective load carrying area for acompressive load C centrally applied and bulge free area progressivelyincreases with radii. Accordingly, for a given compressive load C, thecompressive stress and strain are much greater on the innermost layer13. Likewise for a torque T, the greatest shear stress and strain are onthe innermost layer 13. The result is preferential fatigue at theinnermost layer 11.

The problems in these prior art laminated bearings have been recognizedto some extent as evidenced by Orain, U.S. Pat. No. 2,995,907 and Boggs,U.S. Pat. No. 3,377,110. Both of these references teach altering theshape of the bearing, namely length, to adjust the mean circumferentialarea of the outer resilient layers 13 and thus, provide a more uniformshear stress and strain distribution in the resilient layers 13 whensubjected to a cyclic torsional motion to prolong the life of theinnermost resilient layer 13. When graded length is employed touniformly distribute shear stresses and strain, compressive stresses inthe outermost layers is substantially increased. Thus, failure fromexcessive compressive stresses becomes important. Furthermore, stabilityof the bearing under high compressive loads is unfavorable. In addition,such bearings are often inadequate from a compression load capacity orare impractical to manufacture.

By the present invention the shape of the convention laminated bearingcan be retained while substantially enhancing the fatiguecharacteristics of the bearing without substantial sacrifice incompression deflection or compression load capacity. With reference toFIG. 2, there is shown a bearing 20 of the present invention in the formof a sector of a cylinder. As illustrated, bearing 20 comprises an innermember 21 having an outwardly facing convex surface and an outer member22 radially spaced from the inner member 21 and having an inwardlyfacing concave surface. Between and bonded to the members 11 and 12 arealternating bonded layers 23 and 24 of a resilient material such as anelastomer and a non-extensible material such as metal, respectively.Inner and outer members 21 and 22 are identical to members 11 and 12 ofbearing 10. As with bearing 10, the convex and concave surfaces and eachof the layers 23 and 24 are concentrically disposed about a commoncenter and each layer 23 of resilient material has a generally uniformlength. However, rather than layers 23 of a resilient material havinguniform thickness and uniform modulus of elasticity, the thickness ofthe layers 23 progressively increases from the common center while themodulus of elasticity progressively decreases from the common center.This simultaneous grading of thickness and modulus in the resilientlayers 23 has been found to substantially enhance the fatigue life of abearing subject to cyclic torsional motion.

To understand the benefits obtained by the present invention, let usfirst look at the effect of a compressive load C on a bearing. Eachlayer of resilient material in series must carry this compressive loadC. For prior art bearing 10, FIG. 1, having uniform resilient layer 13thickness, the effective load carrying area of each layer increases withincreasing radii. Accordingly, the compressive stresses in the layers 13decreases with increasing radii. With reference to FIG. 3 there is shownthe typical relation between allowable compressive stress and shapefactor for a given compressive load and modulus of elasticity of theresilient material. In the bearing 10, let us suppose the shape factorfor the innermost layer is S, with a compressive stress C₁ and that theshape factor for the outermost layer is S₂. Since the compressive stressC₂ in the outer most layer is less than C₁, the shape factor at theoutermost layer may be reduced to S₃, a value substantially less thanthat provided by bearing 10. One approach, as previously mentioned, isto grade the circumferential area. However, by the present invention, ithas been found most desirable to grade the thickness of the resilientlayers proportionally with radii. If the bearing 20 is to have the sameoverall dimensions of bearing 10, it is seen that by grading thethickness of resilient layers 23 additional resilient material can beused and less non-extensible material. While this approach also reducesto some extent the resistance to compression deflection of bearing 20,the advantages obtained are more than offsetting. By the inclusion ofmore resilient material radially of the bearing within the availablespace, the rotational stiffness of the bearing is decreased to requireless work of the resilient layers in torsion for a given torsionalmotion reducing to some extent the shear stresses and strains on theinnermost resilient layers.

Having considered the compressive stress distribution and the effect ofgrading the thickness of the resilient layers on shear stresses andstrains, let us look in more detail at the bearing in torsion. It can beshown that the torsional or rotational spring rate K_(R) of a spring isgoverned by the equation

    K.sub.R =K.sub.S R.sup.2 where:

K_(S) =spring rate in shear translation, and

R=distance from fixed pivot to center line of spring K_(S).

Thus, for a laminated bearing wherein the layers are concentric about acommon center, all other things being equal, the contribution of theoutermost resilient layers to the rotational stiffness is considerablygreater than the innermost resilient layers. Since the inner resilientlayers are much softer in rotation than the outer resilient layers, themajor portion of the deflection (strain) in torsion will occur at theinner layers, the innermost layer in particular.

The torsional strain in layers of resilient material in a laminatedbearing 30 at different radial distances from the common center areshown in FIG. 4 where 31 designates an inner layer of thickness t₁ andmean radius R₁ and 32 designates an outer layer of thickness t_(n) andmean radius R_(n), each subject to a torque T. Under this torque, theinner layer 31 deflects in shear a distance d₁ or through an angle θ₁and the outer layer 32 deflects in shear a distance d_(n) or through anangle θ₂. The equations giving these strains are as follows:

1. K_(r).sbsb.1 =rotational spring rate of layer 31=(T/θ₁);

2. K_(r).sbsb.n =rotational spring rate of layer 32=(T/θ₂);

3. θ₁ =(d₁ /R₁) where d₁ is the tangential deflection of layer 31;

4. θ₂ =(d_(n) /R_(n)) where d_(n) is the tangential deflection of layer32;

5. e₁ =strain of layer 31=(d₁ /t₁); and

6. e_(n) =strain of layer 32=(d_(n) /t_(n)).

Substituting Equations 3 and 5 in Equation 1 gives:

7. K_(r).sbsb.1 =(TR₁ /d₁)=(TR₁ /e₁ t₁).

Substituting Equations 4 and 6 in Equation 2 gives:

8. K_(r).sbsb.n =(TR_(n) /d_(n))=(TR_(n) /e_(n) t_(n)).

The ratio of Equations 7 and 8 gives: ##EQU1## Substituting the valuesof K_(R) =K_(S) R₁ ² and K_(R).sbsb.n =K_(S).sbsb.n R_(n) ², Equation 9becomes ##EQU2## Substituting in Equation 10 the values of K_(S).sbsb.1=(A₁ G₁ /t₁) and K_(S).sbsb.n =(A_(n) G_(n) /t_(n))

where: A₁ and A_(n) =Surface area of the respective layers 31 and 32;and

G₁ and G_(n) =Shear modulus of the respective layers 31 and 32, Equation(10) becomes: ##EQU3## 12. (A₁ G₁ R₁ /A_(n) G_(n) R_(n))=e_(n) /e₁.

In a given design then Equation 12 means that the strain is a directfunction of area, modulus, and radius. In fatigue applications, then thedesirable thing to have would be a condition where the strain e_(n)across the outer layer 32 is equal to or approaching the strain e₁across the inner layer 31.

Applying the Equation 12 to the layers a and n for a cylindrical or tubeform laminated bearing having length 1,

13. (e_(n) /e_(n))=A_(n) G_(n) R_(n) /A_(n) G_(n) R_(n))=2πR_(a) G_(a)R_(a) /2πR_(n) G_(n) R_(n))=(G_(a) R_(a) 2/G_(n) R_(n) ²) or

14. (G_(n) /G_(n))=R_(n) ² e_(n) /R_(a) ² e_(a)).

From Equation 14 it appears that the strain in layers n and a are equalif the modulus of elasticity varies inversely as the square of the meanradius of the respective resilient layers or (G_(a) /G_(A'),)=(R_(n) ²/R_(a) ²).

It also appears that if the modulus of the layer a is equal to themodulus of the layer n, the strain will vary inversely as the square ofthe radius. For example, when G_(n) =G_(a) and R_(n) =2 and R_(a) =1,e_(a) =e_(n) (R_(n) ² /R_(a) ²)=4_(e).sbsb.n.

Applying equation 12 to the layers x and n of a spherical laminatedbearing:

15. (e_(n) /e_(x))=(A_(x) G_(x) R_(x) /A_(n) G_(n) R_(n))=(2πR_(x) ²G_(x) R_(x) /2πR_(n) ² G_(n) R_(n))=(G_(x) R_(x) ³ /G_(n) R_(n) ³).

From Equation 14 it appears that the strains in layers n and x are equalif the modulus of elasticity varies inversely as the cube of the meanradius of the respective resilient layers of (G_(x) /G_(AH))=(R_(n) ³/R_(x) ³).

It also appears that if the modulus of the layers x is equal to themodulus of the layer n, the strain will vary inversely as the cubes ofthe radius. For example, when G_(n) =G_(x), R_(n) =2 and R_(x) =1, e_(x)=(e_(n) R_(n) ³ /R_(x) ³)=8e_(n).

For the cylindrical laminated bearing, the strain in each resilientlayer is uniform throughout the length. For the spherical laminatedbearing, the strain varies along the length of each layer. This suggeststhat for spherical shapes the spring should occupy less than ahemisphere if permitted by other design requirements.

In practical designs, the variation in strain may be subject tocorrection factors due to variation in the geometry of the springs fromthe simple cylindrical and spherical shapes discussed. These correctionfactors in many instances may be empirically derived from testexperiences. However, in general, it may be stated that for laminatedbearings of the present invention, the fatigue life will be improved ifthe modulus of each layer varies inversely as an exponential of itsradius as given by the following equation: ##EQU4## where M is a numberless than or equal to 1. More generally, it may be stated thatimprovement in fatigue life will be obtained if there is a progressivedecrease in modulus of elasticity of the resilient material withincrease in radii.

The above presentation clearly illustrates that in a laminated bearingcomprising alternating bonded layers of a reslient material and anon-extensible material generally concentrically disposed about a commoncenter with successive layers being disposed at successively increasingradii, it is advantageous to progressively increase the thickness of thelayers of resilient material with increasing radii and to progressivelydecrease the modulus of elasticity of the layers of resilient materialwith increasing radii. By progressively increasing the thickness of thelayers of resilient material with increasing radii more resilientmaterial may be radially disposed within the same space with thecompressive stresses in the resilient layers maintained within allowablelimits. The increased amount of resilient material favorablyredistributes the shear stresses and strains in torsion to enhance thefatigue life thereof. In addition the number of non-extensible laminaeare decreased to reduce the overall weight and cost of manufacture.However, the graded thickness of the resilient layers approach cannot beutilized to optimize the shear-strain distribution. To completeoptimization in design, it is necessary to grade the modulus ofelasticity of the layers of resilient material such that it decreaseswith increasing radii. These two concepts cooperate to provide anoptimum design in a laminated bearing adapted to accommodate relativelylarge cyclic torsional motions while carrying a high compressive load.

By way of illustration, a laminated bearing of the cylindrical or tubeform was designed to carrying a compressive load of 70,000 pounds and toaccommodate a cyclic torsional motion of 7°. The overall length of thebearing was 6 inches. The inside and outside radii were 1.620 and 2.750inches, respectively. In a prior art design, having uniform thicknessand modulus of elasticity in the resilient layer, a calculated fatiguelife of 530 hours resulted. Where the thickness and modulus ofelasticity were simultaneously graded in accordance with the presentinvention with the innermost resilient layer having the same thicknessand modulus of elasticity as that of the innermost layer of the priorart bearing, a calculated fatigue life of approximately 6,200 hoursresulted. Needless to say, the advantage obtained in fatigue life by thepresent invention is quite substantial.

In the drawings and specification, there has been set forth a preferredembodiment of the invention and, although specific terms are employed,they are used in a generic and descriptive sense only and not forpurposes of limitation.

What is claimed is:
 1. A compressive load carrying laminated bearingcomprising alternating bonded layers of a resilient material and anon-extensible material generally concentrically disposed about a commoncenter with successive layers being disposed at successively increasingradii with the thickness of said layers of resilient materialprogressively increasing with radii while the modules of elasticity ofsaid layers of resilient material simultaneously decreases with radii.2. A compressive load carrying laminated bearing comprising an innersupport member having an outwardly facing convex surface, an outersupport member having an inwardly facing concave surface radially spacedfrom the convex surface of said inner member, said convex and concavesurfaces being concentrically disposed about a common center,alternating bonded layers of a resilient material and a non-extensiblematerial disposed between and fixedly secured to the convex and concavesurfaces of said inner and outer members, respectively, said layers ofnon-extensible material being concentrically disposed about said commoncenter, successive layers of said resilient material and non-extensiblematerial being disposed at successively increasing radii with thethickness of said layers of resilient material progressively increasingwith radii while the modulus of elasticity of said layers of resilientmaterial simultaneously decreases with radii. .Iadd.
 3. A compressiveload carrying laminated bearing comprising alternating bonded layers ofaresilient material and a non-extensible material generallyconcentrically disposed about a common center with successive layersbeing disposed at successively increasing radiiwith the thickness ofsaid layers of resilient material progressively increasing with radiiwhile the modulus of elasticity of said layers of resilient materialsimultaneously decreases with radii; said compressive load carryinglaminated bearing having a configuration comprising a generally conical,cylindrical or spherical shape or a segmented form thereof; and saidcompressive load carrying laminated bearing being characterized byextended fatigue life resulting from a concurrent increase in resilientlayer thickness and decrease in modulus of resilient layer elasticitymoving generally radially outward from said common center. .Iaddend..Iadd.
 4. A compressive load carrying laminated bearing comprising aninner support member havingan outwardly facing convex surface, an outersupport member having an inwardly facing concave surface radially spacedfrom the convex surface of said inner member, said convex and concavesurfaces being concentrically disposed about a common center,alternating bonded layers of a resilient material and a non-extensiblematerial disposed between and fixedly secured to the convex and concavesurfaces of said inner and outer members respectively, said layers ofnon-extensible material being concentrically disposed about said commoncenter, successive layers of said resilient material and non-extensiblematerial being disposed at successively increasing radiiwith thethickness of said layers of resilient material progressively increasingwith radii while the modulus of elasticity of said layers of resilientmaterial simultaneously decreases with radii, said compressive loadcarrying laminated bearing having a configuration comprising a generallyconical, cylindrical or spherical shape or a segmented form thereof; andsaid compressive load carrying laminated bearing being characterized byextended fatigue life resulting from a concurrent increase in resilientlayer thickness and decrease in modulus of resilient layer elasticity,moving generally radially outward from said common center. .Iaddend.